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Basic Algebraic Equations

Context for this Lesson


TOPIC: Basic Equations in Real Life

GRADE LEVEL: 6th Grade

FOCUS QUESTION: How can we create a mathematic equation in a real life situation to solve a problem?



§111.22. Mathematics, Grade 6.

(b) Knowledge and Skills

  • (5) Patterns, relationships, and algebraic thinking. The student uses letters to represent an unknown in an equation. The student is expected to formulate equations from problem situations described by linear relationships.
  • (11) Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
    • (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics
    • (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

Common Core State Standards:

Grade 6 Overview

Expressions and Equations: 

  • Reason about and solve one-variable equations and inequalities.
    • (6) Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
    • (7) Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
  • Represent and analyze quantitative relationships between dependent and independent variables
    • (9) Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. 


  • Colored tape 
  • Boom box/Speaker
  • Music.
  • Poster paper with
    • x+y=300
    • 2x=y
    • x+2x=300
    • 3x=300

Add other equations as lesson plan becomes more difficult. An open area with lots of floor space; a gymnasium, classroom where desks have been moved to the side or outside will do. Tape a giant square on the floor. Create four equal squares within the one square. Label two squares x and two squares y.


Activity One:

Let’s start today by walking around the classroom. For now, let’s try not to talk. You can acknowledge your friends, but this is about getting into our own bodies. So, walk around. Play music while they move. Allow the students to walk around for a while. Then stop the music and say freeze. Alright, let’s look around the room. What do you notice about the space and where people are standing? Have the students continue to move, encouraging them to fill the empty spaces. Again freeze and ask what they see. Guide them to use the letters on the grid to describe their locations. Have them dance again, ask the x’s to freeze, then the y’s. Sit down for a moment, to bring the focus in. Tell the students that today they are going to imagine being at a school dance. They are all members of the math club, and are trying to raise money for a cause. Have students brainstorm about what the cause will be.

SHARE info about topic: Explain that today we are going to explore problem solving in real life situations. Sit down for a moment, to bring the focus in. Tell the students that today they are going to imagine being at a school dance. They are all members of the math club, and are trying to raise money for a cause by having a dance-a-thon. Have students brainstorm about what the cause will be.


Procedure: Tell the students to imagine that the taped off area is the dance floor. Explain that they only represent a small percentage of students at the dance. Ask them to dance on the dance floor. They will play freeze dance, music stops after a minute or so, dancers freeze. Ask them to name their location (x or y) Explain that these letters describe areas of the gym. Have the students dance some more and freeze again. Ask them to write down their final location and come sit down. Explain that you are going to come in as someone else who has a problem to solve. Enter as the vice principle unraveling a giant piece of poster board with formulas written on it. The principle needs to know how many students were dancing in the y section, and how many in the x section because the y’s all were vegetarian’s and the x’s were all meat eaters. The problem is, you’ve all been dancing for several hours and if you don’t eat, some of you will start passing out. Or maybe quit before we reach our donations goal. The night is young people. So, the principle wants to order pizza for the dancers, and needs to know how many of each kind to order. There were so many dancers at the party, I don’t want to guess and be wrong. How can we figure this out? Allow student to come up with their own formula and questions. After the students decide on their formula, test it by having the students dance again and freeze again. On the first day, students will work on the simple formula above, however, they will create more complicated formulas as the lesson progresses. Eventually, they will create a formula based on the percentage of the student population that they represent, rather than the twice as many vegetarian’s formula. For example, if there are 30 students in the class and they represent 1/10 of the student population. 30x10=300. If there are 10 x’s but we don’t know how many y’s then (10x10)+10y=300. Possible side-coaching: We know there are 300(# of actual students participating) students at the dance. What do we know? There are a total of 300 students, therefore, #x +#y=300 What do we need to know? We also know that there were twice as many x’s as y’s. What other information will help us find the answer? If we know the # of x’s, what do we do? What if we know the # of y’s? What if we don’t know either of the numbers? Can we make a guess just by looking at the room? They might be able to guess that the number of x’s is larger than the number y’s and begin making educated guesses to the numbers. Possibly answer the phone, discuss with the imaginary principle, get off the phone. Oh no, the pizza parlor is about to close and we place our order right away. This could be useful in guiding students to find solutions under time restraint, but should not be used if the students already seem to be frustrated or feeling under pressure. Trouble-shooting (optional) It’s alright to not always know the answer. There is not one right answer, just different ways of looking at the problem. It’s good to have different perspectives or ideas. What will happen if we guess the wrong number? Transition: Whenever the students get stuck or frustrated, they can always go back to the freeze dance to find new perspective. What do you see? What do we know?




  • What did we learn about problem solving today?
  • So, how do we create a formula?


  • Is there one right way to solve a problem?
  • How do we know what is the best way? 


  • What kind of problems can you think of where you might really need to use an equation to find the solution?


  • Was it difficult for students to make the connection between letters and people?
  • How easy was it to work with math as a language?
  • Did embodying the math change the perception of what math is?
  • Were students able to create their own formula, or did they need more guidance?
  • If they needed more guidance, was this a good introduction into algebraic formulas for them?